Add ground beef, onions, carrots, and celery along with 1 teaspoon salt to a large skillet over medium-high heat and cook, crumbing beef, until beef loses its pink color and vegetables soften. Drain any excess fat.

Push beef mixture away from the center of the skillet. Add garlic and cook for 30 seconds or so until fragrant. Stir into beef. Again, push the beef mixture away from the center of the pan and add the spices: Italian seasoning, red pepper flakes, and paprika (if using). Quickly stir, then add the tomato paste. Cook for about a minute, stirring, until the color has slightly deepened.

Add the beef broth, then the half and half, stirring to incorporate the tomato mixture and the ground beef mixture together. Add the remaining teaspoon salt and stir. The liquid may look slightly separated; that’s ok. Add the pasta, stir it in, and bring to a simmer.

Cook at a good simmer 14 to 16 minutes (check the pasta timing on the box or bag for appropriate timing), gently turning the mixture with a large spoon or spatula if needed, until the pasta is almost to the desired degree of doneness. Turn off the heat. Gently fold in the cheese. Allow to sit for several minutes before serving.

Garnish with additional Parmesan and parsley, if desired.

Note: This dish is at its best when cooked almost al dente; the pasta will continue to cook and absorb liquid as it sits and thicken a bit as the cheese is folded in. (If the sauce has thickened too much for your taste, add a bit of water and gently stir. If the sauce seems to thick after sitting, add a bit more water.